the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Apr 2023
Arithmetic relationships in Earth’s global mean energy flow system
Abstract. Definite ratios and arithmetic relationships can be revealed in Earth’s global mean energy flow system. These ratios are not dataset-specific; they can be found in each global energy budget estimate published in the past decade. In this technical paper we point out these arithmetic structures in assessments based on direct observations and climate models; in global energy and water cycle studies; updated energy budget estimates, several satellite-based data products; up to the most recent quantification of the energy flows in the up-to-date global energy and water exchange (GEWEX) data records. The ratios and the corresponding relationships can be recognized both in the all-sky and clear-sky fluxes, and both for radiative (shortwave as well as longwave) and non-radiative energy flow components in the annual global mean. The accuracy of the found relationships allows us to investigate their physical basis, which is identified in known radiation transfer equations. The proposed equations apply only on a subset of the observationally valid arithmetic ratios; other components, having the same accuracy, remain yet unexplained and are presented here only on empirical grounds.
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Status: closed
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AC1: 'Comment on egusphere-2023-698', Miklos Zagoni, 18 Apr 2023
I am aware of some errors in the manuscript. Just the very first of my references, Wild (2012), is missing from the References list:
Wild, M.: New directions: a facelift for the picture of the global energy balance. Atmos Environ 55, 366-367, 2012.
I am grateful for any further observation.Citation: https://doi.org/10.5194/egusphere-2023-698-AC1 -
CC1: 'Comment on egusphere-2023-698', Brian Mapes, 15 Jun 2023
The author finds that certain ratios of fluxes in Earth’s heat balance are close to integer ratios, which could be understandable from classical gray two-stream equilibrium models dating back to Schwartzschild 1906, where the particular value of the gray optical depth drops out of the algebra. Secondarily, the unit flux of these integer ratios apparently is near observed LWCRF, although I could not follow why physically this might be the case. It is hard for this non-expert to assess the p-value of these numerological coincidences being mere happenstance. At best, might this indicate an undiscovered emergent principle, or a theoretical balance-related must-be whose roots may have been overlooked? Do planetary heat budgets from models reproduce the effect, perhaps even for a range of climates (solar constants, longwave gas compositions, land-sea configurations)? If so, might the greater precision of simulations as opposed to observations help make the case for the profundity or unlikelihood of the numerical coincidences more compelling? One wonders if such highly-averaged energy budgets are available as small datasets from the world's vast corpus of planetary climate simulations, to make these low-dimensional calculations easy. Perhaps ChatGPT knows, or a real radiative energy budget expert? Anyway, there is some intrigue here at first blush, alghough the arguments and interpretations here were not taut enough for this nonspecialist to follow well enough.Citation: https://doi.org/
10.5194/egusphere-2023-698-CC1 -
AC2: 'Reply on CC1', Miklos Zagoni, 15 Jun 2023
Thank you for this comment. The paper might have even stopped at the end of the Introduction, by showing the observed integer ratios on different – model-based, satellite-based and water-cycle-based – global mean energy flow estimates. The primary purpose – and motivation – of this paper is to inform the climate- and atmospheric science-community about this recognition. The most remarkable fit is perhaps in Figure 4, a satellite-based estimate, where all (shortwave and longwave, and even the non-radiative) flux components are close to a small integer ratio within the stated range of uncertainty. I am eager to here expert and nonspecialist comments solely about this ‘atomic’, or periodic, system. The unit flux of these integer ratios is really near the observed LWCRE: although it was not my main motivation to show how this physically might be, but later, when I found some reasonable physical background for the system in the simple two-stream Schwarzschild-approximation, when I transformed the clear-sky equations into their all-sky version, the easiest way was to separate atmospheric (longwave) radiation transfer from the (longwave) cloud radiative effect. Hence, the role of LWCRE as the ‘pacer’ or ‘pacemaker’ simply arose from the creation of the all-sky equation. Evidently, this is neither complete nor compelling explanation. These are the equations, two clear-sky, and their all-sky form (including LWCRE) that were satisfied best the available datasets (for example, the CERES EBAF Edition 4.1 and 4.2, the most recent ones, spanning over more than two decades as shown in my Section 4.6, and the NEWS/GEWEX assessments of the hydrological cycle, as given in Section 4.8, and Figure 8. – In the Discussion (Section 5 of my paper), I show a geometric representation of the equations, which is again a reproduction of the simplest Greenhouse Effect model of the literature from standard university textbooks. Most recently I can add the new book of Kevin Trenberth (2022), where the work of a greenhouse effect is demonstrated on a two-plate model (Page 30, sidebar 3.2, Figure 3.3). There is no surface, only the plates in empty space and the Sun; and, importantly, the two clear-sky equations are valid as well. The integer system is originates from here (see my Figures 10, 11 and 12.). My Table 2 compares the Integers to CERES data and finds each value far within the stated range of CERES uncertainties. – A final support for LWCRE to be the ‘peace-maker’ among the global mean energy flow components is the empirically observed fact that TOA shortwave flux components, not involved in the equations, still occupy integer positions in the system, connected to the measured incoming radiation from the Sun, with LWCRE = 1 unit. –-- Dear Commenter, I hopy this reply was useful.
Citation: https://doi.org/10.5194/egusphere-2023-698-AC2 -
AC3: 'Reply on AC2', Miklos Zagoni, 15 Jun 2023
Regarding the fundamental question, why the unit flux of these integer ratios is LWCRE, one might further ask: which LWCRE, at TOA, or at the surface? Interestingly, the two are observationally very close to each other. In Stephens et al. (2012), the value at TOA is 26.7 ± 4, and at the surface 26.6 ± 5 Wm-2. In CERES observations, LWCRE at TOA is the lower, but according to L’Ecuyer (2019), the surface value is the lower (with a mean value of 26.7 Wm-2). So in my first, observation-based introductory assessment, this mean value represents the longwave connection between clear-sky and all-sky fluxes. --- A geometric model for the TOA incoming and outgoing shortwave radiation as members of the integer ratio system with the same unit flux of LWCRE is proposed in my latest NASA CERES Science Team Meeting presentation (May 2023, 23 min):
https://ceres.larc.nasa.gov/documents/STM/2023-05/MP4files/CERES_STM_Day3_Zagoni_051123.mp4
Citation: https://doi.org/10.5194/egusphere-2023-698-AC3
-
AC3: 'Reply on AC2', Miklos Zagoni, 15 Jun 2023
-
AC2: 'Reply on CC1', Miklos Zagoni, 15 Jun 2023
Interactive discussion
Status: closed
-
AC1: 'Comment on egusphere-2023-698', Miklos Zagoni, 18 Apr 2023
I am aware of some errors in the manuscript. Just the very first of my references, Wild (2012), is missing from the References list:
Wild, M.: New directions: a facelift for the picture of the global energy balance. Atmos Environ 55, 366-367, 2012.
I am grateful for any further observation.Citation: https://doi.org/10.5194/egusphere-2023-698-AC1 -
CC1: 'Comment on egusphere-2023-698', Brian Mapes, 15 Jun 2023
The author finds that certain ratios of fluxes in Earth’s heat balance are close to integer ratios, which could be understandable from classical gray two-stream equilibrium models dating back to Schwartzschild 1906, where the particular value of the gray optical depth drops out of the algebra. Secondarily, the unit flux of these integer ratios apparently is near observed LWCRF, although I could not follow why physically this might be the case. It is hard for this non-expert to assess the p-value of these numerological coincidences being mere happenstance. At best, might this indicate an undiscovered emergent principle, or a theoretical balance-related must-be whose roots may have been overlooked? Do planetary heat budgets from models reproduce the effect, perhaps even for a range of climates (solar constants, longwave gas compositions, land-sea configurations)? If so, might the greater precision of simulations as opposed to observations help make the case for the profundity or unlikelihood of the numerical coincidences more compelling? One wonders if such highly-averaged energy budgets are available as small datasets from the world's vast corpus of planetary climate simulations, to make these low-dimensional calculations easy. Perhaps ChatGPT knows, or a real radiative energy budget expert? Anyway, there is some intrigue here at first blush, alghough the arguments and interpretations here were not taut enough for this nonspecialist to follow well enough.Citation: https://doi.org/
10.5194/egusphere-2023-698-CC1 -
AC2: 'Reply on CC1', Miklos Zagoni, 15 Jun 2023
Thank you for this comment. The paper might have even stopped at the end of the Introduction, by showing the observed integer ratios on different – model-based, satellite-based and water-cycle-based – global mean energy flow estimates. The primary purpose – and motivation – of this paper is to inform the climate- and atmospheric science-community about this recognition. The most remarkable fit is perhaps in Figure 4, a satellite-based estimate, where all (shortwave and longwave, and even the non-radiative) flux components are close to a small integer ratio within the stated range of uncertainty. I am eager to here expert and nonspecialist comments solely about this ‘atomic’, or periodic, system. The unit flux of these integer ratios is really near the observed LWCRE: although it was not my main motivation to show how this physically might be, but later, when I found some reasonable physical background for the system in the simple two-stream Schwarzschild-approximation, when I transformed the clear-sky equations into their all-sky version, the easiest way was to separate atmospheric (longwave) radiation transfer from the (longwave) cloud radiative effect. Hence, the role of LWCRE as the ‘pacer’ or ‘pacemaker’ simply arose from the creation of the all-sky equation. Evidently, this is neither complete nor compelling explanation. These are the equations, two clear-sky, and their all-sky form (including LWCRE) that were satisfied best the available datasets (for example, the CERES EBAF Edition 4.1 and 4.2, the most recent ones, spanning over more than two decades as shown in my Section 4.6, and the NEWS/GEWEX assessments of the hydrological cycle, as given in Section 4.8, and Figure 8. – In the Discussion (Section 5 of my paper), I show a geometric representation of the equations, which is again a reproduction of the simplest Greenhouse Effect model of the literature from standard university textbooks. Most recently I can add the new book of Kevin Trenberth (2022), where the work of a greenhouse effect is demonstrated on a two-plate model (Page 30, sidebar 3.2, Figure 3.3). There is no surface, only the plates in empty space and the Sun; and, importantly, the two clear-sky equations are valid as well. The integer system is originates from here (see my Figures 10, 11 and 12.). My Table 2 compares the Integers to CERES data and finds each value far within the stated range of CERES uncertainties. – A final support for LWCRE to be the ‘peace-maker’ among the global mean energy flow components is the empirically observed fact that TOA shortwave flux components, not involved in the equations, still occupy integer positions in the system, connected to the measured incoming radiation from the Sun, with LWCRE = 1 unit. –-- Dear Commenter, I hopy this reply was useful.
Citation: https://doi.org/10.5194/egusphere-2023-698-AC2 -
AC3: 'Reply on AC2', Miklos Zagoni, 15 Jun 2023
Regarding the fundamental question, why the unit flux of these integer ratios is LWCRE, one might further ask: which LWCRE, at TOA, or at the surface? Interestingly, the two are observationally very close to each other. In Stephens et al. (2012), the value at TOA is 26.7 ± 4, and at the surface 26.6 ± 5 Wm-2. In CERES observations, LWCRE at TOA is the lower, but according to L’Ecuyer (2019), the surface value is the lower (with a mean value of 26.7 Wm-2). So in my first, observation-based introductory assessment, this mean value represents the longwave connection between clear-sky and all-sky fluxes. --- A geometric model for the TOA incoming and outgoing shortwave radiation as members of the integer ratio system with the same unit flux of LWCRE is proposed in my latest NASA CERES Science Team Meeting presentation (May 2023, 23 min):
https://ceres.larc.nasa.gov/documents/STM/2023-05/MP4files/CERES_STM_Day3_Zagoni_051123.mp4
Citation: https://doi.org/10.5194/egusphere-2023-698-AC3
-
AC3: 'Reply on AC2', Miklos Zagoni, 15 Jun 2023
-
AC2: 'Reply on CC1', Miklos Zagoni, 15 Jun 2023
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